Recent%20Beam-Beam%20Simulation%20for%20PEP-II

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Recent Beam-Beam Simulation for PEP-II

• Yunhai Cai
• December 13, 2004
• PEP-II Machine Advisory Committee Meeting at SLAC

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• Acknowledgment
• Beam-beam study group
• John Seeman (PEP-II, SLAC)
• Witold Kozanecki (PEP-II, BaBar)
• Ilya Narsky (BaBar, Caltech)
• Frank Porter (BaBar, Caltech)
• Nonlinear map
• Yiton Yan (ARDA, SLAC)
• Benchmark codes
• Kazuhito Ohmi (KEKB)
• Masafumi Tawada (KEKB)
• Joe Rogers (CESR, Cornell)

• Outline
• New PC cluster
• Nonlinear maps
• Closed orbit and tune shift due to parasitic
  collision
• Crossing angle and parasitic collision
• Intensity
• Year of 2007
• Conclusion

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SLAC PC FARM

• Linux cluster interconnected with 64-bit PCI-X
  (PCIXD, Lanai X) Myrinet 2000.
• All nodes are 2.6GHz dual-Xeon Pentium IV
  Rackable systems running RHEL 3.0.
• These are 128 of our 384 node Linux cluster.
• 20 faster than seaborg at NERSC for beam-beam
  simulation using 32 processors.
• We own 25 of the cluster.

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Scaling on Parallel Supercomputers

• Recently, SLAC has installed a Linux clusters
  with 128 processors. We have high priority on the
  cluster because of our contribution 50,000 to
  the purchase.

SP(IBM), T3E(CRAY), ALVAREZ (LINUX PC) are the
super computers at NERSC. We gain a factor of
24 In speed with 32 processors on the SP.
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Main Features in the Code Beam-Beam Interaction
(BBI)

• Arbitrary beam distributions
• Precision Poisson solver for the core
• Equal-spacing or equal-area longitudinal slices
• Linear interpolation between the slices
• Numerical convergence in all three dimensions
• Radiation damping and quantum excitation
• Linear or nonlinear map for the lattices
• Gaussian beam-beam kicks
• Parallel supercomputing with 32 processors
• Crossing angle and parasitic collisions
• Object-oriented in C with MPI library

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PEP-II with a Crossing AngleOctober 9, 2003
For a half angle of 3.0 mrad, we see a
degradation of luminosity by 43. Similar results
have been obtained by Ohmi and Tawada using
their code.
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Luminosity Reduction due to Parasitic
CollisionsApril 15, 2004
7.125x1030cm-2s-1
The smaller by makes more degradation to the
luminosity In terms of the absolute values but
not in relative ones. The reduction is about 7
in both cases. With 1412 bunches, we can achieve
1x1034 cm-2s-1 when by 7mm without Increasing
beam currents.
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Comparison of map and element-by-element tracking
(5sy/step)
6th order
8th order
Taylor map (Zlib)
Mix-variable generating
function (Zlib)
element-by-element tracking (LEGO)
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Parameters Description(5/21/2004) LER(e) HER(e-)
E(Gev) beam energy 3.1 9.0
N bunch population 6.97x1010 (1.52mA) 4.40x1010 (0.96mA)
bx(cm) beta x at the IP 32 32.0
by(cm) beta y at the IP 1.05 1.05
ex(nm-rad) emittance x 22.0 59.0
ey(nm-rad) emittance y 1.40 1.30
nx x tune 0.5162 0.5203
ny y tune 0.5639 0.6223
ns synchrotron tune 0.029 0.049
sz(cm) bunch length 1.30 1.15
sp energy spread 6.5x10-4 6.1x10-4
tt(turn) transverse damping time 9800 5030
tl(turn) longitudinal damping time 4800 2573
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PEP-II Parasitic CollisionsMay 21, 2004
crossingm dxmm of s(e) of s(e-)
0.32 0.1 0.84 0.51
0.63 3.22 17.38 10.61
0.95 9.69 36.87 22.51
1.26 17.78 52.16 31.85
1.58 28.86 68.28 41.69
1.89 43.6 86.75 52.97
2.21 60.53 103.38 63.13
2.52 77.61 116.52 71.15
2.84 94.73 126.41 77.19
3.15 112.31 135.28 82.61
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Head-on Collision and Parasitic Collisions

• Head-on collision is calculated with
  particle-in-cell method
• Gaussian approximation is used for parasitic
  crossing and beam size is updated every 1000
  turns
• Only the nearest parasitic crossings are included
• Drift is used between the parasitic collisions
  and head-on collision

dx
Tune shift from parasitic collision
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Tune Shift Due to Parasitic Crossings
LER(e) HER(e-)
Horizontal -0.000958 -0.000523
Vertical 0.0233(0.026) 0.0123(0.014)
Two nearest parasitic collisions are included in
the calculation. Single parasitic collision
contributes half of the value.
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Closed Orbit at the Interaction point due to
Parasitic Collisions

• Horizontal kick
• Nominal bunch

IP
or
y
Packman bunch
2np-y
e 3.81 mm, 1.40 mrad e- 2.07 mm, 0.78 mrad
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Closed Orbits due to Parasitic Collisions in
Beam-Beam Simulation
x0x0-0
The angles of the orbits are so small that they
do change the luminosity in the simulation.
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Luminosity Effects of Parasitic Collisions and
Its Compensation
Luminosity degradation due to parasitic
collisions is about 5.
The luminosity degradation can be completely
recovered by the tune shifts in vertical plane
for the machine parameters, May 21, 2004.
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Tune shift can be corrected by resetting the tune
when the separation is larger enough compared
to the beam size.
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Tune shift seen in the spectrum is consistent
with the analytic calculation.
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Parasitic Collisions and Crossing Angle at PEP-II
Compared with the measured luminosity 5.61 1030
cm-2s-1, the simulation result with -0.2mrad is
closer.
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Trade off between Parasitic Collisions and
Crossing Angle
Best luminosity achieved when the vertical beam
sizes are small and matched.
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Dependency of Beam Currentswith Parasitic
Collisions and Crossing angle (-0.2mrad)
8x1030
Luminosity
5x1030
Specific Luminosity
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Beam Blowup as Currents Increasewith Parasitic
Collisions and Crossing Angle (-0.2mrad)
Beam-beam scan at low current
Luminous region from BaBar
Blowup of beams
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Beam-Beam Parameters with Parasitic Collisions
0.08
0.06
0.20
May 21, 2004
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Parameters Description(2007, Seeman) LER(e) HER(e-)
E(Gev) beam energy 3.1 9.0
N bunch population 12.03x1010 (2.62mA) 5.88x1010 (1.28mA)
bx(cm) beta x at the IP 28 28.0
by(cm) beta y at the IP 0.8 0.8
ex(nm-rad) emittance x 60.0 60.0
ey(nm-rad) emittance y 1.0 1.0
nx x tune 0.5162 0.5203
ny y tune 0.5639 0.6223
ns synchrotron tune 0.032 0.055
sz(cm) bunch length 0.9 0.9
sp energy spread 6.5x10-4 6.1x10-4
tt(turn) transverse damping time 9800 5030
tl(turn) longitudinal damping time 4800 2573
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PEP-II Parasitic CollisionsYear of 2007
crossingm dxmm of s(e) of s(e-)
0.32 0.1 0.51 0.51
0.63 3.22 10.09 10.09
0.95 9.69 21.14 21.14
1.26 17.78 29.76 29.76
1.58 28.86 38.85 38.85
1.89 43.6 49.30 49.30
2.21 60.53 58.70 58.70
2.52 77.61 66.12 66.12
2.84 94.73 71.71 71.71
3.15 112.31 76.72 76.72
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Tune Shift Due to Parasitic CrossingsYear of 2007
LER(e) HER(e-)
Horizontal -0.00139 -0.00098
Vertical 0.0406 0.0286
Two nearest parasitic collisions are included in
the calculation. Single parasitic collision
contributes half of the value. Values are nearly
doubled compared to ones in 2004.
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Luminosity Degradation due to Parasitic
Collisions (Year of 2007)
-76
Without parasitic collisions, the total
luminosity 1715x1.51x1031 cm-2s-1
2.59x1034cm-2s-1 compared to Seemans expected
value 2.4x1034cm-2s-1.
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Tune and Crossing Angle Compensation for
Parasitic Collisions
1.55x1031
Expected luminosity can be achieved with tune
compensation and small crossing angle
(-2x0.5mrad).
dx 3.85 mm at f -0.5mrad (3.22mm at f 0)
which is about 12 sx separation.
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Crossing Angle and More Separation
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Really Need Crossing Angle?
Yes. It helps litter but main gain is from the
separation!
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Future Work

• Detailed tune scan near half integer tune
• All possible machine errors, including coupling
  and dispersions
• Symplectic tracking of non-linear map
• Calculate beam-beam lifetime with nonlinear maps
  parasitic collisions
• More study of upgrades scenarios
• Combined effects of electron cloud and beam-beam

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Conclusion

• Progress has been made to symplectify Taylor map.
  The improvement of computational speed allows us
  to include machine nonlinearity in the beam-beam
  simulation. This is critical for beam-beam
  lifetime calculation.
• For current parameters, the luminosity
  degradation due to the parasitic collisions is
  about 5 which can be simply recovered with a
  change of the vertical tunes.
• Our simulation confirms the experimental
  observation that there is a possible trade off
  between a larger separation of parasitic
  collisions and small crossing angle.
• For 2007 machine parameters, the degradation of
  luminosity is much large, about 75. However, the
  simulation shows that the degradation can be
  partially recovered by resetting the vertical
  tunes and full recovery requires further
  separation of beams at parasitic crossing point
  to 3.85 mm (12 sx). Under these conditions, the
  simulation confirms that Johns expected value of
  luminosity can be achieved.

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Expectations and Suggestions

• lowering of bx(50cm-gt32cm) in the LER should
  be backed out because it increases bx and beam
  size at the parasitic collision points and makes
  beams more mismatched in the head-on collision.
• We should see stronger effects of parasitic
  collisions once wigglers is turned on. That
  implies that we may need to separate beams sooner
  rather than later.
• Parasitic collision may prevent us from moving
  closer to the half integer because the dynamic
  beta and emittance increase the beam size at
  parasitic crossings.
• We suggest to have more experiments to measure
  these effects and compare them to our simulation.